Question

A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side. Also find which shape encloses more area?​

Answer 1

Area of rectangle = L×B

= 40×22

= 880 sq. cm

perimeter of rectangle= 2(l+b)

= 2× (40+22)

. =2× 62

=124 cm

perimeter of rectangle= perimeter of square

Perimeter of square = S ×4

124 cm. = S ×4

124÷4 = S

31 = S

Area of square. = S×S

= 31×31

=961 sq. cm

So, it's clear that area of square (961sq. cm) is greater than area of rectangle (880sq. cm)

Answer 2

Answer:

Given: Length = 40 cm, Breadth = 22 cm Perimeter of the rectangle

= Length of the wire

= 2(l + b) = 2(40 cm + 22 cm)

= 2 × 62 cm = 124 cm

Now, the wire is rebent into a square.

Perimeter = 124 cm

⇒ 4 × side = 124

∴ side = $\frac{124}{4}$ cm = 31 cm

So, the measure of each side = 31 cm

Area of rectangular shape = l × b

= 40 cm x 22 cm

= 880 cm^2

Area of square shape = (Side)^2

= (31)2 = 961 cm2

Since 961 cm^2 > 880 cm^2

Hence, the square encloses more area.

Step-by-step explanation: